Question

In triangle ABC, line joining the circumcenter and orthocenter is parallel to side AC, then the value of tan A tan C is equal to
A. `sqrt3`
B. 3
C. `3sqrt3`
D. none of these

Answer 1

Correct Answer - B
The distance of circumcenter from side AC is `R cos B`, and the distance of orthocenter from side AC is `2R cos A cos C`. Therefore,
`R cos B = 2R cos A cos C`
`:. Cos (A +C) = 2 cos A cos C`
`:. sin A sin C = 3 cos A cos C`
`:. tan A tan C = 3`